Abstract
The problem of computing bounds on the region-of-attraction for systems with polynomial vector fields is considered. Invariant subsets of the region-of-attraction are characterized as sublevel sets of Lyapunov functions. Finite-dimensional polynomial parametrizations for Lyapunov functions are used. A methodology utilizing information from simulations to generate Lyapunov function candidates satisfying necessary conditions for bilinear constraints is proposed. The suitability of Lyapunov function candidates is assessed solving linear sum-of-squares optimization problems. Qualified candidates are used to compute invariant subsets of the region-of-attraction and to initialize various bilinear search strategies for further optimization. We illustrate the method on small examples from the literature and several control oriented systems.
Original language | English (US) |
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Pages (from-to) | 2669-2675 |
Number of pages | 7 |
Journal | Automatica |
Volume | 44 |
Issue number | 10 |
DOIs | |
State | Published - Oct 1 2008 |
Keywords
- Local stability
- Nonlinear dynamics
- Region-of-attraction
- Simulations
- Sum-of-squares programming